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The value of tan{(cos^(- 1)(-2/7)-pi/2)]...

The value of `tan{(cos^(- 1)(-2/7)-pi/2)]` is

Text Solution

Verified by Experts

The correct Answer is:
`(2)/(3sqrt5)`
`tan {(cos^(-1)(-(2)/(7)) - (pi)/(2))}`
`= tan {pi - cos^(-1) ((2)/(7)) - (pi)/(2)}`
`= tan {(pi)/(2) - cos^(-1) ((2)/(7))}`
`= tan {sin^(-1) ((2)/(7))}`
`= tan tan^(-1) ((2)/(3sqrt5)) = (2)/(3sqrt5)`
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